Preheat your oven to 350 degrees. Spray a large rimmed baking tray (10 by 15) with cooking spray and set aside.
In a large bowl whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, cloves, ginger and salt.
In a medium bowl, whisk together the eggs, sugars, oil, and apple sauce until smooth.
Stir the liquid ingredients into the flour mixture until just combined. Then stir in the carrots.
Pour the cake batter into the prepared baking sheet. Bake for 20 to 25 minutes or until the edges of the cake are golden and starting to pull away from the baking sheet. Be careful not to overbake.
While the cake is cooling, cream together the cream cheese and the butter in the bowl of a stand mixer. Add the powdered sugar one cup at a time. Then add in the vanilla extract.
Once the cake is cool to the touch, spread the frosting over the top. If you desire, sprinkles chopped pecans around the edge. Cut, serve, and enjoy. Cover the left overs with aluminum foil and store in the refrigerator for up to one week.